TSTP Solution File: SET927+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:48:05 EDT 2023
% Result : Theorem 3.84s 4.00s
% Output : Proof 3.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14 % Command : duper %s
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 15:23:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 3.84/4.00 SZS status Theorem for theBenchmark.p
% 3.84/4.00 SZS output start Proof for theBenchmark.p
% 3.84/4.00 Clause #4 (by assumption #[]): Eq
% 3.84/4.00 (Not
% 3.84/4.00 (∀ (A B C : Iota),
% 3.84/4.00 Iff (Eq (set_difference (unordered_pair A B) C) (singleton A)) (And (Not (in A C)) (Or (in B C) (Eq A B)))))
% 3.84/4.00 True
% 3.84/4.00 Clause #5 (by assumption #[]): Eq
% 3.84/4.00 (∀ (A B C : Iota),
% 3.84/4.00 Iff (Eq (set_difference (unordered_pair A B) C) (singleton A)) (And (Not (in A C)) (Or (in B C) (Eq A B))))
% 3.84/4.00 True
% 3.84/4.00 Clause #17 (by clausification #[5]): ∀ (a : Iota),
% 3.84/4.00 Eq
% 3.84/4.00 (∀ (B C : Iota),
% 3.84/4.00 Iff (Eq (set_difference (unordered_pair a B) C) (singleton a)) (And (Not (in a C)) (Or (in B C) (Eq a B))))
% 3.84/4.00 True
% 3.84/4.00 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 3.84/4.00 Eq
% 3.84/4.00 (∀ (C : Iota),
% 3.84/4.00 Iff (Eq (set_difference (unordered_pair a a_1) C) (singleton a)) (And (Not (in a C)) (Or (in a_1 C) (Eq a a_1))))
% 3.84/4.00 True
% 3.84/4.00 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.00 Eq
% 3.84/4.00 (Iff (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a))
% 3.84/4.00 (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1))))
% 3.84/4.00 True
% 3.84/4.00 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.00 Or (Eq (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) True)
% 3.84/4.00 (Eq (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1))) False)
% 3.84/4.00 Clause #21 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.00 Or (Eq (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) False)
% 3.84/4.00 (Eq (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1))) True)
% 3.84/4.00 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.00 Or (Eq (And (Not (in a a_1)) (Or (in a_2 a_1) (Eq a a_2))) False)
% 3.84/4.00 (Eq (set_difference (unordered_pair a a_2) a_1) (singleton a))
% 3.84/4.00 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.00 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a))
% 3.84/4.00 (Or (Eq (Not (in a a_2)) False) (Eq (Or (in a_1 a_2) (Eq a a_1)) False))
% 3.84/4.00 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.00 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a))
% 3.84/4.00 (Or (Eq (Or (in a_1 a_2) (Eq a a_1)) False) (Eq (in a a_2) True))
% 3.84/4.00 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.00 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a a_2) True) (Eq (Eq a a_1) False))
% 3.84/4.00 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.00 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a a_2) True) (Eq (in a_1 a_2) False))
% 3.84/4.00 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.00 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a a_2) True) (Ne a a_1))
% 3.84/4.00 Clause #28 (by destructive equality resolution #[27]): ∀ (a a_1 : Iota), Or (Eq (set_difference (unordered_pair a a) a_1) (singleton a)) (Eq (in a a_1) True)
% 3.84/4.00 Clause #29 (by clausification #[4]): Eq
% 3.84/4.00 (∀ (A B C : Iota),
% 3.84/4.00 Iff (Eq (set_difference (unordered_pair A B) C) (singleton A)) (And (Not (in A C)) (Or (in B C) (Eq A B))))
% 3.84/4.00 False
% 3.84/4.00 Clause #30 (by clausification #[29]): ∀ (a : Iota),
% 3.84/4.00 Eq
% 3.84/4.00 (Not
% 3.84/4.00 (∀ (B C : Iota),
% 3.84/4.00 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) B) C) (singleton (skS.0 2 a)))
% 3.84/4.00 (And (Not (in (skS.0 2 a) C)) (Or (in B C) (Eq (skS.0 2 a) B)))))
% 3.84/4.00 True
% 3.84/4.00 Clause #31 (by clausification #[30]): ∀ (a : Iota),
% 3.84/4.00 Eq
% 3.84/4.00 (∀ (B C : Iota),
% 3.84/4.00 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) B) C) (singleton (skS.0 2 a)))
% 3.84/4.00 (And (Not (in (skS.0 2 a) C)) (Or (in B C) (Eq (skS.0 2 a) B))))
% 3.84/4.00 False
% 3.84/4.00 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota),
% 3.84/4.00 Eq
% 3.84/4.00 (Not
% 3.84/4.00 (∀ (C : Iota),
% 3.84/4.00 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) (singleton (skS.0 2 a)))
% 3.84/4.00 (And (Not (in (skS.0 2 a) C)) (Or (in (skS.0 3 a a_1) C) (Eq (skS.0 2 a) (skS.0 3 a a_1))))))
% 3.84/4.00 True
% 3.84/4.00 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota),
% 3.84/4.00 Eq
% 3.84/4.00 (∀ (C : Iota),
% 3.84/4.00 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) (singleton (skS.0 2 a)))
% 3.84/4.00 (And (Not (in (skS.0 2 a) C)) (Or (in (skS.0 3 a a_1) C) (Eq (skS.0 2 a) (skS.0 3 a a_1)))))
% 3.84/4.00 False
% 3.84/4.00 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Eq
% 3.84/4.02 (Not
% 3.84/4.02 (Iff
% 3.84/4.02 (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 3.84/4.02 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))))))
% 3.84/4.02 True
% 3.84/4.02 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Eq
% 3.84/4.02 (Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 3.84/4.02 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1)))))
% 3.84/4.02 False
% 3.84/4.02 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or
% 3.84/4.02 (Eq (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 False)
% 3.84/4.02 (Eq
% 3.84/4.02 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 3.84/4.02 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))))
% 3.84/4.02 False)
% 3.84/4.02 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or
% 3.84/4.02 (Eq (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 True)
% 3.84/4.02 (Eq
% 3.84/4.02 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 3.84/4.02 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))))
% 3.84/4.02 True)
% 3.84/4.02 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or
% 3.84/4.02 (Eq
% 3.84/4.02 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 3.84/4.02 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))))
% 3.84/4.02 False)
% 3.84/4.02 (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 (Or (Eq (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) False)
% 3.84/4.02 (Eq (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))) False))
% 3.84/4.02 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 (Or (Eq (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))) False)
% 3.84/4.02 (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True))
% 3.84/4.02 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) False))
% 3.84/4.02 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False))
% 3.84/4.02 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.02 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Ne (skS.0 2 a) (skS.0 3 a a_1)))
% 3.84/4.02 Clause #44 (by clausification #[21]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or (Eq (And (Not (in a a_1)) (Or (in a_2 a_1) (Eq a a_2))) True)
% 3.84/4.02 (Ne (set_difference (unordered_pair a a_2) a_1) (singleton a))
% 3.84/4.02 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Eq (Or (in a_1 a_2) (Eq a a_1)) True)
% 3.84/4.02 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Eq (Not (in a a_2)) True)
% 3.84/4.02 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a_1 a_2) True) (Eq (Eq a a_1) True))
% 3.84/4.02 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.02 Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a_1 a_2) True) (Eq a a_1))
% 3.84/4.05 Clause #50 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Eq (in a a_2) False)
% 3.84/4.05 Clause #53 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or
% 3.84/4.05 (Eq
% 3.84/4.05 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 3.84/4.05 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))))
% 3.84/4.05 True)
% 3.84/4.05 (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 (Eq (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))) True)
% 3.84/4.05 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 (Eq (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) True)
% 3.84/4.05 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 (Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) (Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) True))
% 3.84/4.05 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 (Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) (Eq (skS.0 2 a) (skS.0 3 a a_1)))
% 3.84/4.05 Clause #58 (by forward contextual literal cutting #[57, 48]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) (Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.84/4.05 Clause #60 (by superposition #[58, 26]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.84/4.05 Or (Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.84/4.05 (Or (Eq (set_difference (unordered_pair a_2 (skS.0 3 a a_1)) (skS.0 4 a a_1 a_3)) (singleton a_2))
% 3.84/4.05 (Or (Eq (in a_2 (skS.0 4 a a_1 a_3)) True) (Eq True False)))
% 3.84/4.05 Clause #62 (by clausification #[55]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False)
% 3.84/4.05 Clause #63 (by forward contextual literal cutting #[62, 50]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False
% 3.84/4.05 Clause #64 (by backward demodulation #[63, 43]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 (Or (Eq False True) (Ne (skS.0 2 a) (skS.0 3 a a_1)))
% 3.84/4.05 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 (Ne (skS.0 2 a) (skS.0 3 a a_1))
% 3.84/4.05 Clause #66 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.84/4.05 Or (Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.84/4.05 (Or (Eq (set_difference (unordered_pair a_2 (skS.0 3 a a_1)) (skS.0 4 a a_1 a_3)) (singleton a_2))
% 3.84/4.05 (Eq (in a_2 (skS.0 4 a a_1 a_3)) True))
% 3.84/4.05 Clause #73 (by forward demodulation #[42, 63]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 (Or (Eq False True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False))
% 3.84/4.05 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)))
% 3.84/4.05 (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False)
% 3.84/4.05 Clause #75 (by superposition #[74, 66]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.84/4.05 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True)
% 3.84/4.05 (Or (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False)))
% 3.84/4.05 Clause #80 (by eliminate resolved literals #[75]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.05 Or (Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.84/4.05 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False))
% 3.84/4.06 Clause #81 (by forward demodulation #[80, 63]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.06 Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) (Or (Eq False True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False))
% 3.84/4.06 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False)
% 3.84/4.06 Clause #83 (by superposition #[82, 58]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) (Or (Eq False True) (Eq (skS.0 2 a) (skS.0 3 a a_1)))
% 3.84/4.06 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) (Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.84/4.06 Clause #85 (by eliminate duplicate literals #[84]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1)
% 3.84/4.06 Clause #94 (by backward contextual literal cutting #[85, 65]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.06 Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))
% 3.84/4.06 Clause #96 (by forward demodulation #[94, 85]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.06 Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 2 a)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))
% 3.84/4.06 Clause #97 (by superposition #[96, 28]): ∀ (a a_1 a_2 : Iota),
% 3.84/4.06 Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a)))
% 3.84/4.06 Clause #98 (by eliminate resolved literals #[97]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True
% 3.84/4.06 Clause #99 (by superposition #[98, 63]): Eq True False
% 3.84/4.06 Clause #102 (by clausification #[99]): False
% 3.84/4.06 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------